Predictive models on COVID 19: What Africans should do?

In this study, predictive models are proposed to accurately estimate the confirmed cases and deaths due to of Corona virus 2019 (COVID-19) in Africa. The study proposed the predictive models to determine the spatial and temporal pattern of COVID 19 in Africa. The result of the study has shown that the spatial and temporal pattern of the pandemic is varying across in the study area. The result has shown that cubic model is best outperforming compared to the other six families of exponentials ( R 2 = 0.996 , F = 538.334 , D F 1 = 3 , D F 1 = 7 , b 1 = 13691.949 , b 2 = - 824.701 , b 1 = 12.956 ) . The adopted cubic algorithm is more robust in predicting the confirmed cases and deaths due to COVID 19. The cubic algorithm is more superior to the state of the art of the works based on the world health organization data. This also entails the best way to mitigate the expansion of COVID 19 is through persistent and strict self-isolation. This pandemic will sustain to grow up, and peak to the highest for which a strong care and public health interventions practically implemented. It is highly recommended for Africans must go beyond theory preparations implementations practically through the public interventions. .

Introduction

Background of the study

Rendering to Nature, a spatial spreading of COVID-19 is attractive overwhelming and has already extended the necessary the standard health benchmarks for the virus to be acknowledged a pandemic, with high infection more than 1.5 million people in 170 countries (Callaway, 2020). On January 7th, 2020, a potential coronavirus was quarantine and considered as severe acute; respiratory syndrome COVID 19, where this virus is considered as COVID 19 by the WHO on February 11th, 2020. The suspections of this novel and potential virus have been regarded and related to the to ABO blood group. For example, Norwalk virus and Hepatitis B have clear blood group susceptibility (Batool et al., 2017; Lindesmith et al., 2003). The spatial distribution of COVID 19 has ready taken on pandemic rate; impacting almost over 170 regions in a matter of several weeks a global reaction to prepare health systems to meet this unprecedented challenge. Thereby, a synchronized global reaction is greatly needed to prepare coordinated health systems so as to attain this unparalleled major areas challenge. There are still growing up of expansion countries that have been unsuccessful adequate to have been vulnerable to these diseases already have, illogically, very appreciated lessons to pass this critical time. Though the suppression measures implemented in China have at least for the current moment reduction to the coming new cases by more than 90%, this reducing is not the case in other Europeans and other African countries (The Economist, 2020). Therefore, cogently known the spatial and temporal modeling, prediction rate of its distribution along with its mitigation mechanisms are very important to give some information in the future to mitigate this serious problem. COVID 19 is becoming the world problem for health, depletion of economy and terrorizing the world, unexpected death and hundred thousands of illness. This work is aimed to determine the spatial and temporal distribution, prediction of death rate and mitigation mechanisms of COVID 19: The Case of Africa. Additionally, we also proposed predictive models on COVID 19 in Africa.

In the present paper, we present adopted mathematical models for COVID-19 that incorporates both potential parameters, including both the environment-to-human and human-to-human routes. Temporarily, the diffusion rates in our model depend on the epidemiological status and the confirmed cases and deaths with time. In particular, when the infection level is high, people would be motivated to take necessary action to reduce the contact with the infected individuals and contaminated environment so as to protect themselves and their families, leading to a reduction of the average transmission rates. We adopted two algorithms both are quadratic and curved exponential process to examine the prediction of confirmed and death rates of COVID 19. There is no a clear indication of the source of the COVID 19, but some recently published works such as (Huang, Wang, Li, & et al, 2020a, 2020b; Chen et al., 2020a; Li et al., 2020a, Li et al., 2020b; Song et al., 2020; Chen et al., 2020b; Wang, Hu, Hu, & et al, 2020a, 2020b; YuanIDWen et al., 2019; ZhouTing et al., 2020; Verity et al., 2019; Shereen et al. Siddique) indicates as the source of the outbreak belongs to Huanan Seafood whole market. Therefore, the foremost contribution novel ideas of the up-to-date are: An efficient and effective prediction models to predict the confirmed number of cases and deaths of the COVID 19. Improved quadratic and curved models are proposed as compared with the other exponential families (logarithmic, logistic, compound, growth and exponential). Therefore, developing a new robust algorithm is very essential to predict the pandemic.

Materials and methods

Study area and period

This study is mainly focusing in Africa where the data are obtained from the daily world health organization.

Source of data

The nature of data related to this study is purely secondary data obtained from the world health organization. Thereby, all the updated information and data related for this study is obtained from the (World Health Organizations, 2020). The prominent information for the study is based on the confirmed number of cases, number of deaths, and the transmission type, which are conveyed on daily registered by the world health organization. The appropriate data for this study is depending on the world health organization.

Robust algorithms

In order to maintain the ultimate goal of this work, we also employed several Evaluations of the Measures such as the cubic, logarithmic, exponential families. The effectiveness of the adopted methods are evaluated based on the using a performance statistical index. This is determined using the result of coefficient of determination is considered to examine the performance of the adopted algorithms as compared to the state of the art of the works. This can be obtained through, the coefficient of determination where is the total number of observations, and are represents forecasted and the observed values, respectively. The ultimate goal of this work is to assess the ability of the quadratic and cubic distribution to predict the COVID 19 through comparison of the other approaches, namely the logarithmic, logistic, curved, compound and exponential models.

Results and discussions

In this section the descriptive and inferential results are cogently addressed. First, the descriptive results are briefly explained. Following this, the inferential results assisted through the predictive models are succeeded. Within this data two potential variables (confirmed cases and deaths) are taken into consideration for this study.

Spatial pattern of COVID 19

This study reveals about 1048, 156 confirmed cases and 55,143 deaths are taken into account worldwide, from the global assessment this is considered as very high risk. From the descriptive results, we noted that the spatial pattern of confirmed number cases of COVID-19 and deaths are both varying with high spread. This entails the distribution of this novel virus across worldwide both in death rate and confirmed cases is varying almost all countries in the world. We rely on the daily reported aggregated data across the globe on two main predictors: the confirmed number cases and deaths. We emphasize the significance of the confirmed cases that is not included in public and private media as broadly as the confirmed cases or the deaths. Therefore, completely two data distributions display an increment in America, the patterns of the deaths were also increased in European (Fig. 1).

Fig. 1

The Spatial distribution of COVID 19 Worldwide based on the Confirmed Cases.

Spatial distribution of CoVID-19 in Africa

A spatial distribution of COVID 19 across the world is varying and growing up alarmingly. As noted in the following figure, the spatial distribution of COVID 19 is varying where the confirmed cases are almost growing up in South Africa, Burkina Faso and Ghana. As the number of entering into Africa is very recent, the confirmed cases are high in Africa and spatially varying (Fig. 2).

Fig. 2

The Spatial distribution of COVID 19 based on Confirmed Cases in Africa.

Predictive models

To predict confirmed number of infections of COVID 19, additionally we considered several prediction approaches. We create predicts using some prediction models with an exponential family (Hyndman et al., 2002; Taylor, 2003). This finding has entailed showing good prediction precision over different prediction mechanisms (Makridakis et al., 1982, Makridakis and Hibon, 2000, Makridakis et al., 2020). Exponential related approaches can take into consideration a variability of pattern and prediction so as to accurately predict the confirmed cases and deaths, then we can give a due a attention for Africa to mitigate its spatial and temporal distributions. Remarkably, unless we give a strong care in combating its mitigation, and develop an effective method, the pattern of this virus will remain danger for human beings even in the future. The proposed method also resembles to the other modeling methods to COVID 19 through an S-Curve algorithms (logistics curve, logarithmic, exponential, compound and the growth curves) that assumes convergence. Thus, all these approaches can be assessed using two different datasets related to COVID 19 on confirmed cases and death rates.

Prediction estimates of confirmed infections of COVID 19

Based on the January 27, 2020, 2798 infected individuals had tested positive for coronavirus disease and 80 deaths. Additionally, as of March 18, 2020, 206,250 patients and 8593 deaths outreached across the world, which cogently reveals the temporal distribution of COVID 19 is going very fact and covering the entire world alarmingly. The recent breakthrough in the temporal distribution of this novel virus pointed out by April 3, 2020 more than one million confirmed cases with more than a half of a million deaths widespread almost in part of the world. But, the estimated death rates are relying on the number infected patients to the total number of peoples died of the potential virus, which does not represent the real fact of the death rate. Notably, the full denominator remains unknown because asymptomatic cases or patients with very mild symptoms might not be tested and will not be identified. Such cases therefore cannot be included in the estimation of actual mortality rates; since actual estimates pertain to clinically apparent COVID-19 cases (Fig. 2). The spatial distribution of COVID 19 In the study area is more and more. This figure cogently illustrates as the temporal distribution of COVID 19 is going very fast and alarmingly (See Fig. 2). This period also based on the recent works (Backer et al., 2020; Huang et al., 2020a, 2020b; eport of theO-Ch, 2020), indicated the supreme nurture time is expected to be up to 14 days, while the middle time from the onset of the patients characteristics and signs to severe care unit (ICU) charge is around 10 days. Yi-Cheng Chen et al, [35 [ proposed a time based vulnerable infected-recovered (SIR) algorithm and the result has shown that the one day forecast mistakes for the numbers of confirmed cases are almost fewer than 3% excepting for the day when the meaning of confirmed cases is altered. In addition to this, WHO report have shown that the time that the symptoms from the onsets and deaths that are ranged within 2 weeks–8 weeks.

Seven different approaches cubic, exponential, quadratic, compound, logarithmic, logistic, Growth and Exponential distributions are considered to accurately estimate the prediction of number of confirmed cases and death rates. From Figure below, we can see that the values along the x-axis indicate duration time indicating days from January 27, 2020. The values along y axis are the confirmed cases of COVID 19. Different literature reviews focused on the under-estimation of coronavirus number of cases; while major surveys by Zhao and collaborators (Zhao et al., 2020) and by Read et al. (Read et al., 2020). Specifically, Zhao and coworkers (Zhao et al., 2020) more pointed out on the assessments under-reporting rate of coronavirus number of cases, through building the epidemic growing curves such as an exponential growing Poisson process. We repeated the process as aforementioned but this can be attained through fitting modeling the data on confirmed number cases between January 27th and April 3, 2020 (Fig. 3) and the dot points are the observed of confirmed cases where the cubic and quadratic curve are both better fit in estimating the confirming cases of COVID 19 as compared to logarithmic, compound, growth, logistic and exponential using the exponential curve growing Poisson process. Adam J Kucharski et al. (Li et al., 1101), proposed a combined a stochastic transmission model, showing that COVID 19 spreading approaches are probably reduced in Wuhan since the late January 2020, but our findings have revealed the number of confirmed cases is highly increased as the duration of time is (Fig. 3.)

Fig. 3

Best fitting of the model to the data of cumulative confirmed cases between 27, January 2020 and 3, April 2020.

Performance of predictive approaches based on confirmed cases

There are several adopted predictive approaches to examine prediction of confirmed cases due to the impending influence of COVID 19. In this section, the performance of the Cubic, curved, quadratic, Logarithmic, Compound, Exponential and logistic are adopted to predict the confirmed cases and deaths. This entails as the shown in Table 1 that the presentation of cubic and quadratic are outperformed as compared methods in based on coefficient of determination. This finding has shown that the proposed algorithm can enhance the variables of the cubic approach efficiently and producing a convenient result through the result attained from the performance measures (Table 1).

Table 1

Performance of Confirmed Cases of COVID 19 using various approaches.

Models Summary along with the Parameter Estimates
Dependent Variable: Confirmed Cases of COVID 19
	R Square	F	df1	df2	Sig.
Logarithmic	.582	12.521	1	9	.006
Compound	.821	41.153	1	9	.000
Growth	.821	41.153	1	9	.000
Exponential	.821	41.153	1	9	.000
Logistic	.821	41.153	1	9	.000
Quadratic	.958	91.230	2	8	.000
Cubic	0.996	538.334	3	7	.000

Prediction estimates of death rates COVID 19

The descriptive result has pointed out as there is still temporal variation of death of COVID 19 with an alarm growing. The temporal distribution of death rate is exponentially increasing across the globe, from which a serious attention is required to mitigate its expansion in Africa in the future. It is an amazing growth especially temporally from month to month with an alarm growth (Fig. 4).

Fig. 4

The temporal distribution of deaths of COVID 19.

But several adopted approaches are also implemented its prediction of the death rate, from which we can note that cubic and quadratic approaches are both better fit the death related data as compared to the other exponential families. The adopted models has shown that the COVID-19 disease infection rate increases more than an exponentially. Our findings is more resembled to the latest work which has shown that the model converges to a maximum number as time increases, indicating a limited impact of COVID-19 (Li et al., 1101). But, the results attained from our work indicates, the deaths is increasing in cubic and quadratic form as shown in Fig. 5. Brandon Michael et al. (_Michael_Henry and _Lippi, 2019) based on Meta findings or analysis, with more than 1389 COVID-19 patients, of which 273 (19.7%) are considered as severe disease (_Michael_Henry and _Lippi, 2019; Guan et al., 2020; Liu et al., 2020; Wang et al., 2020a, 2020b; Zhang et al., 2020). Moreover, Bin Zhao et al. (Li et al. Zhao), has suggested as the results of the sensitivity analysis show that the time it takes for a suspected population to be diagnosed as a confirmed population can have a significant impact on the peak size and duration of the cumulative number of diagnoses. Xinmiao Rong et al. (RongLiu et al., Fan) proposed a new algorithm, from which a sensitivity findings and the simulations results reveals that, enhancing the ratios of timely judgment and shortening the waiting time for diagnosis cannot eradicate COVID 19. This notes, the death and spatial confirmed cases of COVID 19 across the globe is growing in alarm way, the African must give a care and work on its mitigations.

Fig. 5

Model fitting in the prediction.

Performance of predictive approaches to predict death rates

The performance evaluation of the prediction models relying through comparing the findings obtained between adopted methods and other models to predict the deaths as shown in Table 2. It can be concluded that the cubic and quadratic approaches are both outperforms to the other exponential families. Furthermore, the cubic method has the largest coefficient of determination indicating the observed values and the fitted curve are almost overlapping as compared to all the other comparison algorithms (quadratic, logistic, logarithmic, compound, growth and exponential), and pointing with high quality in predicting the death rates. Meanwhile, the quadratic models suggested and ranked as the 2nd, which indicates superior results as compared to the other algorithms. Additionally, the results obtained from the coefficient of determination has again shown that good relationship between the predicted attained by the adopted methods and the observed confirmed cases of COVID 19, which is almost 0.994. Thereby, it also entails as the result is more consistent to the results attained from Fig. 5, which illustrates the data through the proposed algorithms based on the historical data of the COVID-19 death rate. Therefore, for an abnormal growth of cases like the COVID 19, it can be suggested that the cubic mathematical approach has a high potential and more robust to predict the COVID 19 relied dataset.

Table 2

Performance of death rates of COVID 19 using various approaches.

Model Summary and Parameter Estimates
Dependent Variable: Deaths
	R Square	F	df1	df2	Sig.
Logarithmic	.543	10.677	1	9	.010
Compound	.877	64.467	1	9	.000
Growth	.877	64.467	1	9	.000
Exponential	.877	64.467	1	9	.000
Logistic	.877	64.467	1	9	.000
Quadratic	.994	79.212	2	8	.000
Cubic	.994	414.215	3	7	.000

Discussions

In this work, numerous concerns are addressed expressly, in the facet of the source of the outbreak, characteristics and symptoms of the patients, and also the pattern along with the spatial and temporal distribution indicates a strong remark for the developing countries. The result from the descriptive below has indicated as the COVID 19 patient above 40 years old needs a strong care especially in Africa as the infection fatality ratio in increasing exponentially (Fig. 6). This is also strongly supported as the age of 42.2% infected patients are 80–89 years, while nearly about 32.4% are 70–79 years, 8.4% are 60–69 years, and 2.8% are 50–59 years. The ratio of males to females is 80%–20% as the median ages for women (85 years for women versus 80 years for men). The trend in mitigation of COVID 19 in Italians is good in theory, as they are than better than other countries to fight the novel virus however, the strongly recommended as an hostile approach requirements to be taken with infected patients who are disapprovingly ill with COVID 19, often including ventilator support (N JD FLQ et al., 2009).

Fig. 6

Age distribution of infection fatality ration per 1000.

In this discussion section, following these descriptive results, the prediction rates of some potential predictive factors are also addressed as given in the following table (Table 3). The result shown in (Zhao et al. Zho) has shown that a significantly high risk is observed with blood group A for COVID-19 with 1.279 odd ratio (95% CI 1.136–1.440), while a low risks of blood type O for COVID 19 with 0.680 odd ratios along with the confidence interval of (95% CI 0.599–0.771). However (Jonathan et al., 2019), noted as yet in the initial days of the outbreak of COVID 19 and there are a number of uncertainties in both the measure of the current outbreak, as well as the main epidemiological data concerning transmission. But, the speed and the rapidity of the progress of cases since the acknowledgement of the outbreak are much superior to that observed in outbreaks of the other virus. This is reliable with our larger prediction of the generative number for this outbreak compared to these other emergent coronaviruses, suggesting that containment or control of this virus may be significantly more problematic. To tackle the spread of this novel virus (Chen et al., 2019), revealed as the 2019-nCoV infection was of clustering onset, are more likely to affect older males with comorbidities, and can result in severe and even fatal respiratory diseases such as acute respiratory suffering syndrome. In addition to this, the middle ages of those who expired in Italy was 81 years while about greater than more than two thirds of these infected patients had heart pressure, diabetes, HIV infected patients, cardiovascular diseases, or cancer, or were former smokers (Remuzzi & Remuzzi, 2020). This table shown above cogently indicates as both old age and comorbidity proved the common risk factors for predicting death in 49 COVID 19 Patients. In support, COVID-19 related death was associated with old age (60 years, RR = 9.45; 95% CI, 8.09–11.04), male (RR = 1.67, 95% CI, 1.47–1.89) and any comorbidity (5.86; 95% CI, 4.77–7.19), most notably CVD (6.75; 95% CI, 5.40–8.43) followed by hypertension (4.48; 95% CI, 3.69–5.45) and diabetes (4.43; 95% CI, 3.49–5.61). In addition, medical staff had a lower fatality rate than non-clinical staff for COVID-19 (RR = 0.12; 95% CI, 0.05–0.30) (R MH NS KK H, 2016; N JD FLQ et al., 2009) (Table 3).

Table 3

Comparison of risk factors for death due to COVID 19.

Predictive factors		N	CFR, n (%)	RR (95%)
Age	Above 60 years	13909	829 (6)	9.45 (8.09–11.04)
	Below 60 years	30763	194 (0.6)
Sex	Male	22981	653 (2.8)	1.67 (1.47–1.89)
	Female	21691	370 (1.7)
Any comorbidity				5.86 (4.77–7.19)
	Present	5446	273 (5.0)
	Absent	15536	133 (0.9)
Health care worker	Yes	1716	5 (0.3)	0.12 (0.05–0.30)
	No	42956	1018 (2.4)
Hypertension	Yes	2683	161 (6.0)	4.48 (3.69–5.45)
	No	18299	245 (1.3)
Diabetes	Yes	1102	80 (7.3)	4.43 (3.49–5.61)
	No	19880	326 (1.6)
CVD	Yes	873	92 (10.5)	6.75 (5.40–8.43)
	No	20109	314 (1.6)
Cancer	Yes	107	6 (5.6)	2.93 (1.34–6.41)
	No	20875	400 (1.9)
Other factors	Respiratory disease			3.43 (2.42–4.86)
	Cerebrovascular disease			5.34 (2.34–12.16)
	Respiratory disease			3.1 (2.6–4.2)

The way forward and forthcoming directions to mitigate the spatial COVID 19 in Africa

The spatial and temporal distribution of COVID 19 is dispersing on across the world globally alarmingly, where the growth in death and number of confirmed cases are still continuing in Africa. Pervasive and well known actions are taken to decrease human to diffusion of COVID 19 are required to mitigate the current outburst in Africa. Several European countries such as Italians, the Spanish and UK are good in theory; but, they lack in responding in an aggressive approach to casting out the virus (Remuzzi & Remuzzi, 2020; Verity et al., 2019). As we have lack of health facility and human resource, the Africans must seek distinct courtesy and efforts to mitigate or decrease transmission must be implemented in vulnerable populations including youngsters, children, women’s, health care providers, and elders. Additionally, the African guideline must prepare strong guideline on its medical staff, healthcare providers, and public health individuals and researchers, which is more resembled as in (Habte TadesseLikassa, 2020; Jin et al., 2020). The growth prediction rate of confirmed cases and death rate of COVID 19 is seems more cubic and quadratic, as such as the distribution of this growing up alarmingly the joint team is needed for Africans to give a strong awareness for African community. Strong attention is highly recommended especially for an early death cases of COVID-19 outbreak occurred primarily in elderly people, possibly due to a weak immune system that permits faster progression of viral infection (Jin et al., 2020; Wang et al., 2020d, Wang et al., 2020c). Thus, Africans must give a due attention in these areas where highly spreading is occurred to mitigate the expansion of this potential virus, and giving an aggressive response to this virus is the most fundamental issue. Physical contact with wet and contaminated objects should be considered in dealing with the virus as an alternative route of transmission (Assiri et al., 2013; Lee et al., 2003). As it is observed in Wuhan, China and we also observed in another countries counting the US have implemented major preventing and important controlling actions including travel screenings to control additional distribution of the virus (Carlos et al., 2020), as such all African countries must come together jointly to strongly work on mobility and tackle the spreading of the novel virus through a strong prevention and controlling mechanisms. Epidemiological changes in COVID-19 infection should be monitored taking into account potential routes of transmission and subclinical infections. To diminish fright and monetary harm, and to cogently accomplish and save the infection, much continue to be done in mitigating the spatial and temporal distribution of COVID 19. The Africans must work in cooperation to reduce its distribution so to disruption the transmission shackle of COVID 19. This will also entails to bring an efficient and an effective program to trace, diagnose, and cure an infected patients needs a due attention with regard to patient’s previous health history, travelling experience, different blood types. It is of great authoritative that we call for global action to deal with this major public health emergency.

Conclusion

This research is proposed the predictive models on COVID 19 in Africa. Thereby, it also assesses the spatial and temporal pattern of the COVID 19 so that strong intervention is needed for an action to be taken. The result has shown that the spatial and temporal distribution of COVID 19 is varying across the world, where the confirmed cases and deaths getting started to high in Africa. The results also pointed out, the fitting effects of cubic and quadratic models are the best among all the aforementioned methods, while the fitting effect of cubic model outperform to all family of an exponentials. The result has shown that the cubic algorithm is better predicts the confirmed cases and the deaths of COVID 19 as compared to the other baselines algorithms (. A more robust and effective preventing techniques are needed to take a strong actions so that the spread of the virus is alleviated through expanding more health facilities (increasing accessible number of hospital beds, a strong unity and collaboration of all leaders). Africans must united together to mitigate the spatial spread of the pandemic to reduce the deaths and human life losses.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.